The mathematical theory of tangles, the centrepiece of the celebrated Robertson-Seymour theory of graph minors, finds precise structure in imprecise data. Assuming only basic undergraduate mathematics, this book shows how tangles can identify, relate, and structure types in data: of behaviour, political views, texts, or proteins.
The mathematical theory of tangles, the centrepiece of the celebrated Robertson-Seymour theory of graph minors, finds precise structure in imprecise data. Assuming only basic undergraduate mathematics, this book shows how tangles can identify, relate, and structure types in data: of behaviour, political views, texts, or proteins.
Reinhard Diestel is Chair of Discrete Mathematics at Universität Hamburg, where he works on structural graph theory and combinatorics. He is the author of the leading graduate-level text 'Graph Theory' (6th edition, 2024), which has been translated into German, Russian, Japanese, and Chinese.
Inhaltsangabe
Part I. Tangles - A New Paradigm for Clusters and Types: 1. The idea behind tangles 2. The notion of a tangle 3. The two main tangle theorems: an informal preview Part II. Tangles in Different Contexts - A Collection of Informal Examples: 4. Examples from the natural sciences 5. Examples from the social sciences 6. Examples from data science Part III. The Mathematics of Tangles - Concepts, Theorems, Algorithms: 7. The formal setup for tangles 8. Tangle theorems 9. Order functions 10. Choosing the feature system 11. Algorithms Part IV. Applying Tangles - Back to the Examples: 12. Applying tangles in the natural sciences 13. Applying tangles in the social sciences 14. Applying tangles in data science Notes References Symbol index Subject index.
Part I. Tangles - A New Paradigm for Clusters and Types: 1. The idea behind tangles 2. The notion of a tangle 3. The two main tangle theorems: an informal preview Part II. Tangles in Different Contexts - A Collection of Informal Examples: 4. Examples from the natural sciences 5. Examples from the social sciences 6. Examples from data science Part III. The Mathematics of Tangles - Concepts, Theorems, Algorithms: 7. The formal setup for tangles 8. Tangle theorems 9. Order functions 10. Choosing the feature system 11. Algorithms Part IV. Applying Tangles - Back to the Examples: 12. Applying tangles in the natural sciences 13. Applying tangles in the social sciences 14. Applying tangles in data science Notes References Symbol index Subject index.
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